How can I get the last 5 element of this tax query?

add the ‘date_query’ parameter to your query and include the current year.

$args = array(
  'post_type' => 'news',
  'posts_per_page' => 5,
  'post_status' => 'publish',
  'order' => 'ASC',
  'tax_query' => array(
     array(
      'taxonomy' => 'week',
      'field' => 'slug',
      'terms' => date("W", strtotime("this week")),
    )
  ),
  'date_query' => array(
    array(
      'year'  => date("Y")
    )
  )
);